can someone pls tell me the steps or ideas or materials or hints on how to obtain the moment generating function,probability generating function,cumulant generating function and characteristic function of probability distributions e.g beta distribution etc

Jul 16th 2007, 12:53 PM

CaptainBlack

Quote:

Originally Posted by helpme2007

can someone pls tell me the steps or ideas or materials or hints on how to obtain the moment generating function,probability generating function,cumulant generating function and characteristic function of probability distributions e.g beta distribution etc

there are two ways:

i. Type the relevant terms into wikipedia and perform the given operations

ii. Get a suitable handbook in which they are tabulated (Abramowitz and
Stegun is probably a good place to start.

RonL

Jul 18th 2007, 12:03 PM

BasicIdeaIsSimple

Nice textbook

I like "Probability and Random Processes" by Grimmett and Stirzaker Clarendon press, Oxford, United Kindom. Lots of examples from different areas plus main ideas like moment generating functions, Laplace transform and Fourier.

Jul 18th 2007, 12:27 PM

BasicIdeaIsSimple

Some examples

Characteristic fcn is just probabilists fancy name for Fourier or Laplace transform or some discrete version of this. You use it to calc expected values. This is kind of basic idea. For details see Grimmett & Stirzaker, GS from now.